Question

two boys searching for buried treasure are standing underneath the same tree. One boy walks 18m east and then 18m north. The other boy walks 16m west and then 11m north. What is the scalar product of their net displacements from the ree?

Answer 1

To solve this problem we must simply have the knowledge of scalar product.

Let's define the route of the two people as A and B. Then the first route, the A, would be given by,

We will take the Cartesian plane system as our reference system in which the north is equivalent to the positive sense of the Y axis. And the positive sense of the X will be equivalent to the east.

$A = 18\hat{i}+18\hat{j}$

$B = -16\hat{i} +11\hat{j}$

Making the scalar product we have to,

$A*B = (18\hat{i}+18\hat{j})*(-16\hat{i} +11\hat{j})$

$A*B = (18*16)(18*11)$

$A*B = -288+198$

$A*B = -90$

Therefore the product of their net displacements from the ree is -90.